Several methods for making warm-to-cold current lead connections are described in related art (see Reference 2). One of the most common types of current leads is that of a normal (non-superconducting) metal conductor making the connection from a room temperature reservoir to a lower temperature reservoir in which the primary method of heat transfer is via thermal conduction from the warm reservoir to the cold reservoir and in which (Joule) heat is generated by ohmic conduction caused by current flow in an electrical conductor. The optimum ratio of length (L) to cross sectional area (A) of the current lead (L/A) is found by minimizing the sum of the ohmic heating and heat conduction terms for a given material. The resulting design is a function only of the cold and warm end temperatures, lead material, and current. More information regarding this topic can be found in R. McFee, “Optimum Input Leads for Cryogenic Apparatus,” Rev Scientific Instr., 30 (1959), which is incorporated by reference in its entirety for the purposes of enablement.
A more energy efficient current lead design uses forced flow gas, vapor, or liquid cooling along the length of the lead which from the warmer temperature reservoir to the lower temperature reservoir. A common type of current lead is a so-called “cryogenic vapor cooled lead” in which the vapor evolved from an evaporating liquid cryogen bath (e.g. helium, hydrogen, neon, air, nitrogen, etc.) due to heat influx at the bottom of the current lead flow upwards, exchanges heat with the current lead, and cools the remaining portions of the current lead. A gas or vapor cooled current lead is said to be “optimized” when two boundary conditions are met. First, the gas exiting the current lead is at the same temperature as the temperature reservoir where it is exiting. For example, if the gas is exiting to a room temperature source, then one of the boundary conditions is such that exit gas effluent is also at room temperature. A second boundary condition in an optimize gas cooled current lead is met when the temperature gradient (dT/dx) on one of the ends of the current lead is zero such that there is no net heat flux into the current lead.
A so-called binary vapor cooled current lead is one comprising two different sections. One section is comprised of a normal non-superconducting part and the other part/section is comprised of a superconducting material operating below its superconducting transition temperature Tc. The so-called binary vapor cooled current lead yields a greater reduction in room temperature electrical cooling power than a non-binary vapor cooled lead by replacing the cold end (i.e. T<Tc) current path with superconductors to eliminate ohmic heating. Multistage heat exchangers to intercept heat at the warm end (i.e. T>Tc) can yield still further reductions in cooling power by intercepting heat at higher temperatures, where the Carnot efficiency is higher. If too many heat exchanger intercepts are employed, such systems can become too complex to be practical. A simpler and more efficient concept for cooling current leads is to consider a gas or vapor cooled current lead. This concept is a binary current lead composed of a high temperature superconducting section operating at T<Tc and normal non-superconducting section operating at T>Tc. The normal non-superconducting section/portion of the current lead is cooled through forced convection by a gas cooling fluid (e.g. helium, hydrogen, nitrogen, etc.). There will be a negligible heat flux into the high temperature superconductor as long as the inlet temperature of the cooling fluid is below that of the cold end junction temperature. An earlier design study by R. Wesche and A. M. Fuchs, “Design of Superconducting Current Leads,” Cryogenics, vol. 34, pp. 145-154, February 1994. which is incorporated by reference in its entirety for the purposes of enablement, shows that the option requiring the lowest cooling power is comprised of an HTS section at the cold end (T<Tc) and a gas flow cooled section at the warm end T>Tc (see Reference 2).